Efficient vectorizable PDE solvers

Schönauer, Willi; Weiss, Rüdiger

doi:10.1016/b978-0-444-88621-7.50019-0

Cited by 124 publications

(161 citation statements)

References 5 publications

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“…The numerical calculations were performed with the software package CADSOL, based on the Newton-Raphson method [25]. We have carried out the main part of the numerical analysis for the case of unit vortex number n = 1 in (8) as in Refs.…”

Section: Numerical Resultsmentioning

confidence: 99%

Monopole–antimonopole solutions of the Skyrmed SU(2) Yang–Mills–Higgs model

Paturyan

Tchrakian

2003

Journal of Mathematical Physics

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Section: Numerical Resultsmentioning

confidence: 99%

Monopole–antimonopole solutions of the Skyrmed SU(2) Yang–Mills–Higgs model

Paturyan

Tchrakian

2003

Journal of Mathematical Physics

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“…Typical mesh sizes are N x = 260, N θ = 60. We then employ the CADSOL package [67] based on the Newton-Raphson method. The partial derivatives are discretized with sixth order of consistency.…”

Section: A Numerical Methodsmentioning

confidence: 99%

Rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory

et al. 2016

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We construct sequences of rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory, employing two equations of state for the nuclear matter. We analyze the dependence of the physical properties of these neutron stars on the Gauss-Bonnet coupling strength. For a given equation of state we determine the physically relevant domain of rapidly rotating neutron stars, which is delimited by the set of neutron stars rotating at the Kepler limit, the set of neutron stars along the secular instability line, and the set of static neutron stars. As compared to Einstein gravity, the presence of the Gauss-Bonnet term decreases this domain, leading to lower values for the maximum mass as well as to smaller central densities. The quadrupole moment is decreased by the GaussBonnet term for rapidly rotating neutron stars, while it is increased for slowly rotating neutron stars. The universal relation between the quadrupole moment and the moment of inertia found in General Relativity appears to extend to dilatonic Einstein-Gauss-Bonnet theory with very little dependence on the coupling strength of the Gauss-Bonnet term. The neutron stars carry a small dilaton charge.

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“…A detailed presentation of the this code is presented in [39]. This code requests the system of nonlinear partial differential equations to be written in the form P (x, θ, u, u x , u θ , u xθ , u xx , u θθ ) = 0, (where u denotes the set of unknown functions) subject to a set of boundary conditions on a rectangular domain.…”

Section: Further Remarks Conclusionmentioning

confidence: 99%

Generalized Weyl solutions in d = 5 Einstein-Gauss-Bonnet theory: the static black ring

Kleihaus¹,

Kunz²,

Radu³

2010

J. High Energ. Phys.

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We argue that the Weyl coordinates and the rod-structure employed to construct static axisymmetric solutions in higher dimensional Einstein gravity can be generalized to the Einstein-Gauss-Bonnet theory. As a concrete application of the general formalism, we present numerical evidence for the existence of static black ring solutions in Einstein-Gauss-Bonnet theory in five spacetime dimensions. They approach asymptotically the Minkowski background and are supported against collapse by a conical singularity in the form of a disk. An interesting feature of these solutions is that the Gauss-Bonnet term reduces the conical excess of the static black rings. Analogous to the Einstein-GaussBonnet black strings, for a given mass the static black rings exist up to a maximal value of the Gauss-Bonnet coupling constant α ′ . Moreover, in the limit of large ring radius, the suitably rescaled black ring maximal value of α ′ and the black string maximal value of α ′ agree.

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Efficient vectorizable PDE solvers

Cited by 124 publications

References 5 publications

Monopole–antimonopole solutions of the Skyrmed SU(2) Yang–Mills–Higgs model

Monopole–antimonopole solutions of the Skyrmed SU(2) Yang–Mills–Higgs model

Rapidly rotating neutron stars in dilatonic Einstein-Gauss-Bonnet theory

Generalized Weyl solutions in d = 5 Einstein-Gauss-Bonnet theory: the static black ring

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